CINCINNATI — Mitt Romney, for most of his campaign, mocked President Obama for trying to “transform America.” But in the final days of his race for the presidency, the Republican is driving home a singular message: He, not the president, is the true agent of change.

“We want to bring the real change to America,” Romney said Saturday in Dubuque, Iowa, part of a whirlwind day that also took him to Newington, N.H.; Colorado Springs; and Englewood, Colo. “He says it has to stay this way. I say it can’t stay this way. . . . I want to go to work, he wants to settle.”

Obama, who ran four years ago preaching a fundamental break from politics of the past, campaigns now with the slogan “Forward.” Yet the Democrat also frequently encourages voters to look back, not only at his accomplishments but those of a predecessor.

“Now, for eight years, we had a president who shared our beliefs,” Obama said in Hilliard, Ohio, on Friday. “And his name was Bill Clinton.” Obama chastised Romney for speaking against Clinton’s economic policies — when Romney was running for Senate in 1994.

It has been 521 days since Romney announced his presidential campaign, and 1,384 days since Obama took office. Now hours away from the voters’ verdict, the two are turning to their final arguments, distilled through the lessons of an arduous campaign and presented both to energize the base and to nudge the few undecided voters to their side.

The pitches also illustrate the shifting terrain of both the race and the economy.

The running theory in the Romney campaign had long been that the election would be a referendum on Obama’s handling of the economy. Yet with the number of jobs and consumer confidence both picking up of late, it has started doing more to sell its own candidate as a problem-solver with big ideas.

And Obama, whose campaign has spent much of the past several months ripping into Romney, is spending the final days heralding his own successes in bringing the country back from economic despair.

“We’ve come too far to turn back now,” Obama said on Saturday morning in a suburb of Cleveland, the first stop of a day that later took him to Milwaukee; Dubuque, Iowa; and Bristow, Va. “It’s time to keep pushing forward.”

“I am a long ways away from giving up on this fight,” he added. “I got a lot of fight left in me. I don’t get tired. I don’t grow weary. I hope you aren’t tired either, Ohio.”

Romney, in a stump speech that was retooled and unveiled on Friday, emphasizes unity. After the election, he says, his supporters will not only reach across the street to those who planted Obama signs in their yards, but he will reach across the aisle.

Romney touts his resume, something he had previously mainly left to surrogates. He talks about rescuing the Olympics and alludes to launching Bain Capital.

“I started a business from scratch and helped make it successful,” he said Friday. “That’s not easy.”

Romney also has been putting more emphasis on his four years as Massachusetts governor, saying he was the type of bipartisan bridge-builder that Obama has failed to become.

“I got elected in a state where there are a few Democrats,” Romney told a crowd in Dubuque, where Obama would stop hours later. “Instead of attacking each other, we went to work solving our problems.

“I learned as governor of Massachusetts the best achievements are shared achievements,” Romney added, without mentioning his greatest legislative achievement, the one he took care to include in his official portrait hanging at the State House — health care reform.

Obama’s own record on bipartisanship is often a target.

“You know that if the president is reelected, he will still be unable to work with the people in Congress,” Romney said Friday. “He has ignored them, attacked them, blamed them. The debt ceiling will come up again, and shutdown and default will be threatened, chilling the economy.”

But the biggest shift in Romney’s speech is one that makes him sound like the man he’s running to replace did in 2008. Romney says his campaign is one of both aspiration and new beginnings. He casts himself as the executorof change.

“The question of this election comes down to this: Do you want more of the same or do you want real change?” Romney said Friday. “President Obama promised change, but he could not deliver it. I promise change, and I have a record of achieving it.”

Obama’s message is more complicated now than it was four years ago, when he was running as a break from the past in a way that miffedsome Democrats who took his message as a subtle jab at President Clinton.

Now, Clinton has become the chief surrogate for Obama — they are scheduled to appear together Sunday morning in Concord, N.H. — and Obama frequently talks about the former president.

Obama reminds voters that the country has made progress since 2008, even if it has come slower than he predicted.

“The American auto industry is back on top. Home values are on the rise,” he said Saturday in Ohio. “The war in Iraq is over. The war in Afghanistan is winding down. Al Qaeda is on the run and Osama bin Laden is dead.”

But at the same time, Obama is still trying to make the case that he represents a break from the past. In speeches that were delivered almost simultaneously on Friday — Romney’s in Wisconsin, Obama’s in Ohio — the president used the word “change” 23 times, almost twice as often as Romney.

“Now, Governor Romney, he’s a very gifted salesman. So he’s been trying in this campaign, as hard as he can, to repackage these ideas that didn’t work,” Obama said on Friday. “Have you heard him? He’s going around saying, ‘I’m the candidate of change.’

Romney, he says, is a candidate who changes his positions so often voters cannot tell what he stands for.

“You want to know that your president means what he says and says what he means,” Obama said Saturday in Ohio. “And after four years as president, you know me. You may not agree with every decision I’ve made. You may at times have been frustrated by the pace of change. But you know what I believe.’’

Obama has also spent several minutes at the start of each speech talking about the impacts of Hurricane Sandy, the storm that ravaged New Jersey and New York. It was a time of tragedy, but also of patriotic unity.

“You see heroes running into buildings, wading into the water to help their fellow citizens; neighbors helping neighbors cope with tragedy; leaders of different political parties working together to fix what’s broken,” Obama said Saturday in Ohio. “It’s a spirit that says no matter how bad a storm is, no matter how tough the times are, we’re all in this together — that we rise or fall as one nation, as one people.”

Remarks from the presidential candidates:

President Obama: “We have made real progress”

“The American auto industry is back on top. Home values and housing construction [are] on the rise. . . . Because of the service and sacrifice of our brave men and women in uniform, the war in Iraq is over. . . . Osama bin Laden is dead. We have made real progress.”

. . .

“Now, for eight years, we had a president who shared our beliefs and his name was Bill Clinton. His economic plan asked the wealthiest Americans to pay a little more so we could reduce our deficit and invest in the skills and ideas of our people. And at the time . . . a Senate candidate by the name of Mitt Romney said that Bill Clinton’s plan would hurt the economy.”

. . .

“After four years as president, you know me. You may not agree with every decision I’ve made. . . . But you know what I believe. You know where I stand. You know I tell the truth.”

Mitt Romney: “I will bring people together”

“The question of this election comes down to this: Do you want more of the same or do you want real change? President Obama promised change, but he could not deliver it. I promise change, and I have a record of achieving it.”

. . .

“I built a business, and turned around another. I helped put an Olympics back on track. And with a Democratic legislature, I helped turn my state from deficit to surplus, from job losses to job growth, and from higher taxes to higher takehome pay.”

. . .

“I learned as governor of Massachusetts that the best achievements are shared achievements. I learned that respect and good will go a long way, and are usually returned in kind. That is how I will conduct myself as president. I will reach out to both sides of the aisle. I will bring people together, doing big things for the common good.”

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